Intervention is a better predictor of tDCS mind-wandering effects than subjective beliefs about experimental results

Blinding in non-invasive brain stimulation research is a topic of intense debate, especially regarding the efficacy of sham-controlled methods for transcranial direct current stimulation (tDCS). A common approach to assess blinding success is the inclusion of correct guess rate. However, this method cannot provide insight into the effect of unblinding on observed stimulation outcomes. Thus, the implementation of measures to systematically evaluate subjective expectation regarding stimulation is needed. Previous work evaluated subjective effects in an earlier study which reported a mind-wandering and tDCS data set and concluded that subjective belief drove the pattern of results observed. Here we consider the subjective and objective intervention effects in a key contrast from that data set—2 mA vs. sham—which was not examined in the reanalysis. In addition, we examine another key contrast from a different tDCS mind-wandering study that employed similar methodology. Our findings support objective intervention as the strongest predictor of the observed effects of mind-wandering in both re-analyses, over and above that of subjective intervention. However, it is important to control for and understand the possible inadequacies of sham-controlled methods.

Non-invasive brain stimulation (NIBS) is a popular tool for investigating causal relationships between activity in cortical regions and behaviour 1 . In 2020 the brain stimulation industry was projected to be worth an estimated three billion dollars 2 , a figure that is almost certain to increase in the future. There are multiple methods of NIBS, one of the most common being transcranial direct current stimulation (tDCS 3 ). tDCS typically involves passing electrical current through two electrodes placed on the scalp; a cathode and an anode 4 . Interest has grown in this brain stimulation approach as it can lead to cognitive enhancement both within clinical settings, such as for the treatment of drug-resistant depression 5,6 , as well as in commercial settings via do-it-yourself devices such as the foc.us headset [7][8][9] . A variety of cognitive operations have previously been shown to be influenced by tDCS including: motor 10 and speech motor learning 11 , working memory 12,13 , response selection 14 , multitasking 15 , and attention 16,17 . Given this broad interest there is growing demand for clarity on the efficacy of brain stimulation across the extensive stimulation parameter space.
Although tDCS has been employed extensively, some reviews and meta-analyses [18][19][20] have suggested limited to no effects of transcranial stimulation, with a key focus being on large variability across participants. For example, Lopez-Alonso et al. 19 found only 45% of participants (n = 56) responded to anodal transcranial current stimulation as expected. In an opinion piece, Filmer et al. 3 provide recommendations to insure the reliability, reproducibility, and validity of effects of NIBS studies. Key factors identified by the authors to be addressed include poor methodological design, under-powered samples which give rise to inflated results and, most importantly for the present study, the inadequate blinding of control conditions.
The most common method of blinding in tDCS studies is the sham control method 21 , which mimics the typical initial sensations (i.e., itching or tingling) induced by tDCS by delivering active stimulation for a short period at the beginning (and sometimes again at the end), then either no stimulation or very reduced pulses (which allow some continued sensation) for the rest of the session. Typically, the length of this period of active stimulation is dependent on the stimulation length used for the active condition 22 . It is assumed that sham stimulation controls for any potential unrelated effects of the direct cortical stimulation 22 . However, the efficacy of sham-controlled approaches has been called in to question [23][24][25] . Indeed, in NIBS studies, participants can report perceptual sensations such as visual disturbances, and cutaneous feelings 26,27 . Cutaneous feelings are common in tDCS as seen in a prospective comparison conducted by Kessler et al. 26 with 131 subjects in 277 tDCS sessions. Such feelings were significantly higher in active conditions as compared to sham, for example tingling (89% active vs. 53% sham) and itching (81% vs. 42%). This is potentially a major issue for sham-controlled studies, as observed results may reflect peripheral effects rather than the influence of stimulation on the cortex. Or, put differently, failure of the blinding condition (although, see 28 and 29 ). Another factor that may add to blinding inefficiency is the inadequate reporting of adverse events (such as cutaneous feelings), as this is not only a safety concern but also prevents the experimenter from gaining an understanding of the strength of blinding 27 . Indeed, Wallace et al. 30 found that when investigating the comfort and efficacy of sham-blinding, after a second session of tDCS participants were able to correctly guess stimulation above chance (65%).
A recent paper published by Fassi and Kadosh 31 highlighted possible inadequacies in a common blinding practice in sham-controlled studies, referencing an example from Schecklmann et al. 32 , whilst also bringing attention to studies by Blumberger et al. 33 and Filmer et al. 4 to demonstrate how correct guess rate-the percentage of participants who correctly guess their experimental group-is not an accurate measure of blinding success. Specifically, a hypothetical NIBS experiment was posited, whereby the correct guess rate for both active and sham is 75%, meaning a large majority of the sham condition would have correctly recognised that they did not receive active stimulation 31 , thus demonstrating unblinding of participants. The authors highlight active stimulation guess rate-the percentage of participants who correctly guess they have received active treatment-as a more effective measure of indicating successful blinding, or its failure 31 .
However, a key limitation of active stimulation guess rate (or any guess rate measure) is the inability to reveal the effect blinding (or unblinding) has on the effects and results seen in studies featuring blinding controls, nor does it reveal the direction of these effects. A participant in a sham condition, who believes they are privy to their stimulation condition, could either try to enhance their performance, limit their performance, or have no change in behaviour 34 . A measure of guess rate cannot determine whether this has occurred as they can only reveal the possibility of behavioural changes due to unblinding. Follow-up analyses are needed to investigate these possibilities.
Such a systematic evaluation of subjective expectation of stimulation can be used to address the impact of beliefs regarding stimulation on performance 34 . For example, Fassi and Kadosh 35 used a method of evaluating the effects of participant subjective belief regarding stimulation conditions (i.e. active or sham condition and stimulation intensity), via open-source data from a tDCS mind-wandering study we conducted 4 . The present study also employs this data for a re-analysis, as well as a second mind-wandering study given its methodological similarities 36 .
The two mind-wandering studies featuring tDCS from our lab group 4,36 implemented a sustained attention to response task (SART) with thought probes scattered throughout trials to investigate mind-wandering. Filmer et al. 4 investigated the effect of polarity (anodal and cathodal) and intensity (1 mA and 2 mA) on mind-wandering via tDCS to the left prefrontal cortex, whilst Filmer et al. 36 used the same methodology, polarities, and intensities to investigate the influence of active stimulation to both the prefrontal cortex (PFC) and the inferior parietal lobule (IPL) simultaneously. Both studies measured participant experience after each stimulation session with two questions; whether participants believe they received active or sham stimulation (as a binary choice), and whether they believed they received sham (not applicable), weak, moderate, or strong stimulation.
The key findings for both studies demonstrated modulation of mind-wandering after stimulation; specifically, in Filmer et al. 4 moderate evidence for increased average task-unrelated thoughts (TUT-ratings) after 2 mA cathodal stimulation relative to sham 4 . The two other active conditions cathodal 1 mA and anodal 1 mA failed to produce meaningful results of stimulation on average TUT-ratings, and cathodal 1.5 mA provided anecdotal evidence. For the study by Filmer et al. 36 , anodal stimulation to the left PFC and cathodal stimulation to the right IPL simultaneously at 1 mA produced moderate increases in TUT-ratings relative to sham 36 . Interestingly in this second study, cathodal stimulation to the left PFC and anodal stimulation to the right IPL at 2 mA produced at best anecdotal evidence of an effect of stimulation as compared to sham.
Fassi and Kadosh 35 re-analysed Filmer et al. 4 including the subjective information relating to blinding in the analyses. Specifically, Bayesian ANOVAs compared objective and subjective interventions for mind-wandering across all conditions. They concluded that subjective intervention was a better predictor of participant performance than objective intervention, or a combination of the two 35 . Particularly, those who believed they had received active stimulation had higher levels of mind wandering than those who answered sham. A similar pattern was observed when investigating tDCS dosage: as subjective dosage increased, so did average mindwandering score in a proportional manner. Thus, this finding seemingly calls into question the conclusions of Filmer et al. 4 and, more broadly, those of any study with purely a sham control. However, a key limitation of the Fassi and Kadosh 35 approach was that they examined all conditions on the Filmer et al. 4 study in a single analysis, whereas only effects were observed for cathodal 2.0 mA stimulation as compared to sham comparison with moderate evidence (see Table 1 for specific BF 10 values for the experimental conditions from Filmer et al. 4 ).
The present study sought to re-analyse two existing data sets on mind wandering 4,36 , to account for both subjective and objective beliefs. Here, we used a similar approach as Fassi and Kadosh 35 but with more directed t-tests/paired comparisons, as had been conducted in the two original papers 4,36 . To preview the results, for both re-analyses the objective information regarding stimulation type (active or sham) and dosage (stimulation intensity) was shown to be the best predictor of the influence of tDCS on mind wandering above subjective, or a combination of objective and subjective intervention.  37 . Experimental materials, such as the task, can also be accessed here as well as the demographic and questionnaire data used to establish the experimental measures. For a full overview of the original methods, refer to Filmer et al. 4 .
Subjects. One hundred and fifty subjects (mean age = 23, SD = 5, 96 females) participated in the study. All subjects were right-handed with normal or corrected to normal vision. Subjects were assigned to one of five different stimulation groups based on their participant number sequentially (subject 1, 6, 11 etc. were assigned to anodal stimulation). The final sample per group was 30 4 .
Task. Subjects completed a sustained attention-to-response task (SART), responding via a keyboard key press (space bar) to non-target stimuli (any number except 3). In each trial, a stimulus was presented in the centre of the display. Subjects were to withhold their answer when the target stimulus was presented (the number 3). Stimuli were presented for 1 s and a 1. As previous tDCS studies have demonstrated differential effects of polarity (see 38 and 39 ), the combination of these conditions into the 'weak' category would pose a potentially significant problem given the possibility of these conditions having differential effects on mindwandering thus, we chose to separate them. Given these considerations, objective intervention and objective dosage have the same participants in the same categories, thus can be used interchangeably.
Subjective intervention. Subjective intervention refers to the participants subjective belief regarding the stimulation condition they have been assigned to; either sham or active.
Subjective dosage/intensity. Subjective dosage refers to the perceived strength of stimulation participants believe they have received. Participants indicated that they believed they either received sham, weak, moderate, or strong stimulation.  41 using average mind wandering scores calculated from the whole experimental session for each subject.
To verify both the data and the coding were reproducible, we implemented the statistical analyses of both Fassi and Kadosh 35 and Filmer et al. 4 . All previous findings were replicated. Bayesian statistics and their frequentist counterparts were used as both were included in the previous papers. BF 10 values above 1 provide evidence of H 1 over H 0 ; values below BF 10 1 (or BF 01 ) suggest evidence of H 0 over H 1 . Conventionally, the strength of evidence for a particular hypothesis compared to the competing hypothesis is only regarded as noteworthy when BF 10 values are above 3 and thus any results that fall between 1 and 3 are inconclusive 42 . Often, this is referred to as 'anecdotal evidence' for any given hypothesis, and thus throughout this paper these values will be referred to as such. Values of BF 10 ~ 1 will be considered to provide no evidential value for H 1 over H 0 . BF 01 values 1-3 will be considered as 'anecdotal evidence' for the null hypothesis over H 1 , BF 01 3-10 values as moderate evidence and lastly BF 01 > 10 as strong evidence. When considering values in favour of H 1 over H 0 , as outlined above BF 10 values falling between 1 and 3 will be considered inconclusive or anecdotal (and thus should be interpreted with caution), BF 10 values 3-10 as moderate evidence and BF 10 values > 10 as strong evidence in favour of H 1 . As frequentist statistics were also evaluated, all values of p < 0.05 were accepted as statistically significant.
In JASP (using default priors) we replicated the Bayesian ANOVAs conducted by Fassi and Kadosh 35 however, as previously outlined, only data from the cathodal 2.0 mA and sham condition were included in our key analysis. All relevant post-hoc pairwise comparisons were conducted following each analysis. The first Bayesian ANOVA included objective intervention and subjective intervention as between-subjects factors. To rule out the possibility of subjective information influencing performance in the absence of an effect, this analysis was also performed for each individual condition with no significant effect compared to sham (anodal 1.0 mA, cathodal 1.0 mA and cathodal 1.5 mA). The second Bayesian ANOVA employed objective intervention and subjective dosage as the between-subject factors. Although the authors conducted a third Bayesian ANOVA to investigate the effect of subjective dosage only, we did not include this given the results of the second ANOVA indicating subjective dosage has no evidential value of an effect on mind-wandering.

Results. Summary of the results from Fassi and Cohen Kadosh. We replicated the analyses and findings of
Fassi and Kadosh 35 . When comparing the effect of stimulation intervention, the key finding included subjective intervention (BF inc = 2.442, BF 10 = 3.374, t(148) = 2.55, p = 0.012) being the best predictor of the observed changes in mind-wandering over and above that of objective intervention as compared to sham. In short, following it appears based on this results that subjective participant belief regarding the type of stimulation received (sham versus active) provides a better explanation of participant performance compared to objective intervention, subjective and objective intervention combined or an interaction between the two. The full model result from this ANOVA can be found in the table located in Appendix A1.
For dosage, again, participant belief about stimulation dosage was a better predictor of mind wandering than objective intervention alone, a combination of the two measures or an interaction between them (BF 10 = 3.708 35 ). Fassi and Kadosh 35 did not report the frequentist statistics for this finding however when we replicated the ANOVA we determined the values to be BF inc = 2.685, BF 10 = 3.713, F(3, 146) = 3.829, p = 0.011. The full model table can be found in Appendix A2. When investigating dosage alone, subjective dosage (BF 10 = 5.911, F(3,198) = 4.198, p = 0.007) was also a better predictor of mind-wandering changes over and above that of objective intervention. We could not replicate the finding of BF 10 = 5.911, instead finding BF 10 = 3.713 and attribute this to a difference in data handling, given all other values were able to be replicated.
Effect of subjective belief on mind-wandering via 2.0 mA cathodal stimulation vs sham comparison. We implemented the first Bayesian ANOVA discussed above (employing objective intervention and subjective intervention as between-subject factors and average TUT as the outcome measure), however, crucially, we focussed exclusively on the cathodal 2.0 mA vs the sham comparison as this is the finding Filmer et al. 4 focussed their conclusions on. The full model comparing against the null can be found in Appendix B1 however a summarised model table comparing these results to those of Fassi and Kadosh 35 can be found in Table 2. Here, we observed that objective intervention was the strongest model predictor with moderate evidence (BF inc = 7.437, BF 10 Table 3, which demonstrates that when evaluating only conditions previously found to demonstrate meaningful results, the effect of subjective dosage can no longer be observed. However, given these BF values fall below 1 the null model is considered the best model predictor and these results are inconclusive, providing evidence instead for H 0 . In the absence of an objective effect, subjective information has the potential to be a better predictor of results, and this should be considered by investigators. To wit, even though this was not seen with our data, if a study is inadequately blinded then it is plausible that subjective experience may lead to significant differences in performance, and thus lead to spurious effects where no active control condition is included.

Reanalysis 2: Filmer et al. 36
Methods. The method was identical to re-analysis 1 except where noted.
Data and materials. The study by Filmer et al. 36 was pre-registered via the Open Science Framework with details of analysis plan, methodology and sample size by the authors (osf.io/zvqjb). The raw data from the original study has been made open source by the authors and can be accessed via the UQ eSpace 41 . For a full overview of the original methods, refer to Filmer et al. 36 .
Subjects. One hundred and fifty subjects were recruited for the study (mean age = 22.51, SD = 4.49 and 89 females). Three participants were removed from the initial data set due to equipment malfunctions but were replaced (N = 150). One participant was removed before the re-analysis (N = 149) for guessing both active and sham for subjective intervention.
Task 36 . The SART (Sustained Attention to Response Task) was used. Each block consisted of 6 trials, with each block containing three presentations of the target number and three presentations of the thought probe. Participants completed a short practice block with two trials: responding to one target number and one thought probe, before receiving tDCS. After stimulation, participants completed 8 blocks of the task, each separated by a short break.   36 were first replicated, before a series of one-way Bayesian ANOVAs were conducted to investigate the effect of both objective and subjective stimulation on TUT ratings regarding active conditions relative to sham, dosage, polarity and subjective stimulation intensity. Similar analyses were conducted to investigate the effect of stimulation on Target Accuracy, Non-Target Accuracy and Non-Target Reaction time. One-way ANOVAs were also conducted to investigate the best model fit when comparing objective stimulation, subjective stimulation, and an objective + subjective stimulation for TUT ratings. All relevant post-hoc pairwise comparisons were conducted following each analysis. The same categorisation of results for the Bayesian statistics will be used as in re-analysis 1, as outlined under 'Statistical analysis' .

Results
First and second half analyses were conducted to investigate the relationship between stimulation and mindwandering over time, as it would be expected that the effects of stimulation would be strongest in the first half (first four blocks) as these are closest to the application of the stimulation, as compared to the second half (last four blocks). The results of these analyses followed the pattern of results as outlined below and have thus not been included for brevity. The results below feature the average of each dependent measure over all eight blocks.
Effect of objective stimulation. The results of Filmer et al. 36 were replicated. Relative to sham, a oneway Bayesian ANOVA with stimulation group as the between-subjects factor and average TUT-ratings as the dependent measure revealed anecdotal evidence for an overall main effect of objective group intervention (BF 10  Comparing the effect of objective and subjective intervention. One-way Bayesian ANOVAs evaluated the effect of Objective Intervention, Subjective Intervention, and a combined measure of Objective and Subjective Intervention on average TUT-ratings. This was done individually for each of the four stimulation conditions as compared to sham and the full model for each comparison can be found in Appendix C and D. The strongest evidence was seen for 1 mA +PFC/−IPL configuration as compared to sham for objective intervention (BF inc = 8.811, BF 10 = 9.840, F(1, 56) = 7.117, p = 0.010), demonstrating moderate evidence for accounting for the variance seen over and above that of subjective intervention alone (BF inc = 0.296, BF 10  Lastly, polarity showed anecdotal evidence for configurations at 1 mA (1 mA +PFC/−IPL and 1 mA +IPL/−PFC), as anecdotal evidence was found for an effect of objective intervention (BF inc = 1.641, BF 10 = 1.657, F (1, 56) = 3.644, p = 0.061) over and above that of subjective intervention (BF inc = 0.294, BF 10 = 0.302, F (1, 56) = 0.001, p = 0.975) or combined objective and subjective intervention (Appendix D3). For the configurations at 2 mA (2 mA +PFC/−IPL and 2 mA +IPL/−PFC), anecdotal evidence was demonstrated for subjective intervention (BF inc = 1.533, BF 10 = 1.471, F (1, 55) = 4.298, p = 0.043) over and above that of objective intervention alone (BF inc = 0.590, BF 10 = 0.551, F (1, 55) = 2.130, p = 0.150) or combined objective and subjective intervention (Appendix D4). However, no conclusions can be drawn from these findings, given the relatively low strength of the BF inc values.
Effect of subjective intervention. When evaluating the effect of subjective intervention, one-way Bayesian ANOVAs were used. Across all investigated measures (relative to sham, dosage, polarity, and subjective stimulation intensity) there was little to no evidence of an effect of subjective intervention on average TUT-ratings. Participant ratings of whether they were in the active or sham condition had no effect on average TUT-rating (BF 10  The effect of subjective stimulation intensity on average TUT-rating was also evaluated however no effect was found (BF 10

Discussion
Blinding efficacy has been called into question and reporting of correct guess rate, a common practice in NIBS research, has been highlighted to have possible shortcomings 31 in its ability to provide insight into the success (or failure) of blinding. There have been examples of methods 31,34 that could provide better insight into this issue, one such method being that of Fassi and Kadosh 35 , which was employed to examine the effect of subjective belief, particularly the hypothesis that participants' subjective beliefs about the influence of tDCS on a cognitive task drove the previous results of Filmer et al. 4 on mind-wandering. The authors concluded that subjective intervention, a participant's personal belief about which stimulation condition they received, was a significant predictor of mind-wandering over and above that of objective intervention. Similarly, when investigating dosage, it was concluded that subjective dosage, a participant's personal belief regarding the intensity of stimulation they received was also a better predictor of mind-wandering than objective intervention alone.
However, it can be argued that this was misleading given that Fassi and Kadosh 35 looked at all conditions from Filmer et al. 4 together when only one stimulation condition, cathodal 2.0 mA, produced meaningful effects regarding mind-wandering. In short, it was problematic to evaluate the effect of subjective belief across all stimulation conditions given that this fails to follow up the previous key result. The present study sought to investigate whether the effects described regarding subjective stimulation held once individual key effects were investigated in a re-analysis. In addition, we investigated the effect subjective intervention could have in the re-analysis of another mind-wandering data set from our lab featuring the same SART methodology.
When evaluating only cathodal 2.0 mA compared to sham from Filmer et al. 4 the effects of subjective beliefs about both intervention and dosage no longer are found. Specifically, we observed moderate evidence to support the notion that objective intervention is the strongest predictor of mind-wandering with higher rates of mindwandering observed within the cathodal 2.0 mA condition relative to sham. Interestingly, subjective intervention became the weakest predictor within the model, lesser than that of objective intervention, objective intervention and subjective intervention combined or an interaction of the two.
The same pattern of results was seen for the second re-analysis. Specifically, the key condition that had originally been reported as showing an effect on mind wandering (1 mA +PFC/−IPL) provided moderate evidence for objective intervention as the strongest predictor over and above that of subjective intervention alone or a combination of the two. All other configurations, and the investigation of polarity and dosage failed to demonstrate a meaningful effect of subjective intervention. When you consider the findings from both studies, it is clear that for at least these two mind-wandering studies, participant subjective belief regarding the intervention they received had no effect on the observed changes in mind-wandering.
Despite the present results, the concerns raised about subjective participant beliefs are warranted. Given the thought-provoking critique of the current standard methods of blinding within the literature, more sensitive measures and tests are needed to investigate issues of blinding and subjective belief. Indeed, further investigation of previous data sets and studies within the literature is needed to determine whether these findings have been influenced by participant belief. www.nature.com/scientificreports/ Future studies should implement measures that aim to reduce the effects of subject belief and improve the blinding methods. There is the possibility of implementing methods such as anaesthetic creams to remove the cutaneous feelings entirely from both active and sham conditions, a method that has been successfully used in both animal studies using transcranial alternating current stimulation (tACS) 28 -a similar method to tDCS that involves an oscillating electrical current rather than a direct current 43 -and in humans during tDCS 22,29 . Another consideration is participant experience level, given the findings of Ambrus et al. 21 , who observed that participants who had previous experience with tDCS were more likely to correctly identify trials which featured stimulation and those that featured sham whereas naïve participants were less likely to correctly identify their stimulation condition. This is relatively easy to control through screening processes during recruitment that could help to reduce the unblinding of participants.
Relying on the comparison of a single target condition to a sham condition can be problematic if effective blinding is not achieved, particularly at the participant level as typically participants guess above chance in identifying stimulation conditions 4 . Further, the points raised by Fassi and Kadosh 35 and Filmer et al. 4 , as discussed earlier, support the need for the departure from solely sham controlled methods. The use of active controls or a combination of both active and sham-controlled methods would avoid the issue of unblinding due to perceptual sensation. Active controls also allow for the investigation of the specific role of targeted brain regions when a separate brain region is targeted in the control, or polarity effects when an alternative polarity is applied to the control region 3 . Given the possibility to also investigate hemispheric differences, active controls can provide both a rich comparative measure and interesting investigative opportunities. However, when comparing two active conditions it can be difficult to distinguish which condition is modulating the behaviour when there is a difference between the two conditions, or whether both have an effect. Thus, the most beneficial configuration would be to include a condition of interest, a sham condition and at least one other active control condition, to help mitigate the pros and cons of each technique.
We acknowledge some limitations. First, Filmer et al. 4 did not feature an active control and thus (as outlined previously) is subject to inefficient blinding. We have previously addressed these issues in an opinion paper discussing tDCS efficacy as whole 3 , as well as in subsequent papers. Although no a priori active control conditions were included for either Filmer et al. 4 or Filmer et al. 36 some conclusions can be made about the other active protocols. The 'ineffective' active protocols for Filmer et al. 4 such as the anodal 1.0 mA, cathodal 1.0 mA and cathodal 1.5 mA which demonstrated statistically negligible outcomes on mind-wandering can also be compared to key active conditions. Similarly for the second re-analysis, the findings for +IPL/−PFC were non-substantial and thus can also be compared in this way. Here there is potential for these protocols (and ineffective active protocols in general) to be regarded as active controls, given the statistical differences with key active conditions. Specifically, if there were to be an effect of subjective participant belief on stimulation effects on mind-wandering due to a failure of blinding, it would be expected that these beliefs would generalise to all active conditions, not just one key condition.
However, another limitation to note with this kind of comparison, and of our re-analyses, is the lack of active conditions that differ from one another. The findings of the present re-analysis demonstrate one active group (cathodal 2.0 mA and +PFC/−IPL) that differs from sham, but not an active group that differs from another active group, thus making it difficult to draw definitive conclusions about the role of 'ineffective active protocol' controls.
It is also recognised that the analyses of Fassi and Kadosh 35 were based on the omnibus findings of Filmer et al. 4 and could be argued to follow the pre-registered analysis plan of our original paper more closely. To mediate this issue for the present study, we added a second data set which implements the same stimulation dosages (intensities and duration) as well as the same mind-wandering measures as Filmer et al. 4 . Nowhere do we claim that our blinding method is without fault however after controlling for both objective and subjective intervention, it appears that at least within these two data sets, participant subjective belief of intervention does not meaningfully influence the effects of stimulation on mind-wandering.
The insights and discussions outlined in the present study are facilitated by open science practices and underscore the importance and utility of sharing data. Without these practices, the field would continue to stagnate with poor methodological methods, particularly ineffective blinding, and the discussion of future improvements would be limited. Here we have made the results of Filmer et al. 4 and Filmer et al. 36 more definitive, however this would not have been possible with the insights of Fassi and Kadosh 35 highlighting the benefits of multilab collaboration.

Data availability
The dataset analysed in re-analysis one is available via the UQ eSpace repository